Minimal identities of octonion algebras
type: Item
instance of: scholarly article
title: Minimal identities of octonion algebras
zbMATH Open document ID: 0651.17012
DOI: 10.1016/0021-8693(88)90294-3
author: Michel L. Racine
published in: Journal of Algebra
publication date: 1988-01-01T00:00:00Z
review text: Let \(K\) be a field of a characteristic not \(2, 3\) or \(5\). The main theorem in the paper is an analog of the Amitsur-Levitzki theorem namely: There are no identities of degrees less than 5 for the octonion algebras over \(K\). The author has proved that all identities of degree \(5\) for the octonion algebras follow from the identities \([[x,y]^ 2, z]=0\) and \(x^ 2 S^ +_ 3(y,z,w)-x S^ +_ 3(y,z,w)\circ x=0\) where \(S^ +_ n(x_ 1,...,x_ n)\) is the Jordan standard identity.
reviewed by: Plamen Koshlukov
Mathematics Subject Classification ID: 17D05
Mathematics Subject Classification ID: 16R10
Mathematics Subject Classification ID: 17A50
Mathematics Subject Classification ID: 17A45
Mathematics Subject Classification ID: 17C05
Mathematics Subject Classification ID: 17A60
zbMATH DE Number: 4061462
zbMATH Keywords: polynomial identity
zbMATH Keywords: minimal identities
zbMATH Keywords: Amitsur-Levitzki theorem
zbMATH Keywords: octonion algebras
MaRDI profile type: Publication
full work available at URL: 0021-8693(88)90294-3
OpenAlex ID: W2046448310
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description: scientific article; zbMATH DE number 4061462